Turbulent Particle Flux Research Articles

Effects of collisions on impurity transport driven by electrostatic modes

The turbulence-induced quasi-linear particle flux of a highly charged, collisional impurity species is calculated from the electrostatic gyrokinetic equation including collisions with the bulk ions and the impurities themselves. The equation is solved by an expansion in powers of the impurity charge number $Z$ . In this formalism, the collision operator only affects the impurity flux through the dynamics of the impurities in the direction parallel to the magnetic field. At reactor-relevant collisionality, the parallel dynamics is dominated by the parallel electric field, and collisions have a minor effect on the turbulent particle flux of highly charged, collisional impurities.

Theory of gyrokinetic velocity moment and its application for zonal flows in a tokamak plasma

The calculation of the velocity moment in the gyrokinetic theory and its application in the study of zonal flows in a tokamak plasma are investigated. Based on the scalar invariance property, the expression for the particle velocity in the gyrocenter coordinates is obtained, and a method to systematically calculate the velocity moment in the gyrokinetic theory is proposed, especially for the calculation of the first-order perpendicular velocity moment. The kinetic equation which describes the evolution of the perturbed distribution on the meso-scale of the zonal flow is derived. The effects of the turbulent particle flux, the turbulent energy flux, the turbulent toroidal Reynolds stress and the turbulent poloidal Reynolds stress (PRS) are explicitly included in the phase-space particle flux. In the cylindrical geometry, the zonal radial electric field is driven by the turbulent PRS and the turbulent energy flux, and the result agrees with the radial force balance equation. In the toroidal geometry, the zonal radial electric field is driven by the turbulent PRS, the turbulent energy flux and the turbulent toroidal Reynolds stress; in contrast to the case in the cylindrical geometry, the effect of the turbulent PRS is shielded by the toroidal effect. By combining the radial force balance equation, the poloidal momentum equation in the toroidal geometry is obtained.

Observation of weakly damped modes using high resolution measurement of turbulence in a dipole confined plasma

When plasma is confined by a levitated superconducting current ring, the turbulent radial particle flux changes the direction depending upon the gradient of the particle number within tubes of equal magnetic flux [Garnier et al., Phys. Plasmas 24, 012506 (2017)]. When the density profile is highly peaked, the particle flux is outward. When the density profile is less peaked, turbulence drives an inward “particle pinch.” This change in the direction of particle flux coincides with a reversal of the mean toroidal propagation direction of turbulent fluctuations. Previously, only the mean wavenumber of the fluctuations was reported. The mean wavenumber was computed from the ensemble correlation between two probes. Here, the full frequency-wavenumber power spectrum of the saturated turbulence is calculated by applying Capon's “maximum likelihood method” to floating potential measurements from an array of probes. The power spectrum shows that the highest intensity modes are due to unstable entropy modes, and the less intense modes coincide with weakly damped convective cells, which rotate toroidally in the direction opposite to the unstable modes. Because the weakly damped modes make up a significant fraction of the fluctuating power, these measurements imply that saturated turbulence in a dipole-confined plasma involves the excitation of weakly damped rotating convective cells.

Effect of resonant magnetic perturbation on boundary plasma turbulence and transport on J-TEXT tokamak

The effect of resonant magnetic perturbation (RMP) on boundary turbulence and transport in J-TEXT plasma is experimentally investigated. Edge plasma fluctuations in discharges with and without the (m/n = 3/1) RMP currents are diagnosed by using Langmuir probe arrays. It was found that fluctuations in the edge and scrape-off layer (SOL) regions decrease with the application of a 6 kA RMP. The broadband turbulence at the radial location of which has a characteristic frequency of 40–150 kHz was strongly suppressed when applying RMP, as was the radial turbulent particle flux and blob transport in the near-SOL region. These experimental findings make RMP a promising method of suppressing and controlling turbulence and particle transport in a plasma boundary.

Neural-network-based semi-empirical turbulent particle transport modelling founded on gyrokinetic analyses of JT-60U plasmas

Novel turbulent particle transport modelling has been proposed following joint analyses with gyrokinetic calculations and JT-60U experimental data. Here the diagonal (diffusion) and off-diagonal (pinch) transport mechanisms are treated individually. Besides the decomposition, realistic particle sources from neutral-beam fuelling, which have not been discussed in earlier gyrokinetic studies on particle transport, are taken into account. Taking advantage of the features offered by the modelling, the contribution from each transport mechanism to the turbulent particle flux has been quantitatively clarified. Furthermore, a framework has been developed to calculate the turbulent particle flux driven by each transport mechanism accurately and quickly, taking a neural-network-based approach. The framework can be used for fast prediction of density profiles and for investigating the effects of the transport mechanisms on density profile formation.

Effects of zonal flows on transport crossphase in dissipative trapped-electron mode turbulence in edge plasmas

Confinement regimes with edge transport barriers occur through the suppression of turbulent (convective) fluxes in the particle and/or thermal channels, i.e. , and , respectively, for drift-wave turbulence. The quantity is the turbulence intensity, while and are the crossphases. For H-mode, standard decorrelation theory predicts that it is the turbulence intensity that is mainly affected via flow-induced shearing of turbulent eddies. However, for other regimes (e.g. I-mode, characterized by high energy confinement but low particle confinement), this decrease of turbulence amplitude cannot explain the decoupling of particle versus thermal flux, since a suppression of turbulence intensity would necessarily affect both fluxes the same way. Here, we explore a possible new stabilizing mechanism: zonal flows may directly affect the transport crossphase. We show the effect of this novel mechanism on the turbulent particle flux, by using a simple fluid model (Baver et al 2002 Phys. Plasmas 9 3318) for dissipative trapped-electron mode (DTEM), including zonal flows. We first derive the evolution equation for the transport crossphase δk between density and potential fluctuations, including contributions from the E × B nonlinearity. By using a parametric interaction analysis including the back-reaction on the pump, we obtain a predator–prey like system of equations for the pump amplitude ϕp, the pump crossphase δp, the zonal amplitude ϕz and the triad phase-mismatch Δδ. The system displays limit-cycle oscillations where the instantaneous DTEM growth rate—proportional to the crossphase—shows quasi-periodic relaxations where it departs from that predicted by linear theory.

The effects of magnetic topology on the scrape-off layer turbulence transport in the first divertor plasma operation of Wendelstein 7-X using a new combined probe

Wendelstein 7-X (W7-X) was operated successfully with the first divertor plasma in the operation phase 1.2a (OP1.2a). A new combined probe head, developed and installed on the multiple-purpose manipulator, is able to measure the edge plasma profiles (), variation of magnetic field, poloidal and radial turbulence structures. The scrape-off layer (SOL) plasma parameters in two magnetic configurations (standard and high mirror) are in good agreement with the magnetic island structure and the field line connection length calculated by the field line tracer. In both the standard and high mirror configurations, the radial turbulent heat flux and particle flux have strong dependence on the local magnetic topology, revealing two distinct transport patterns: a broadband turbulence dominant region in the outer SOL and a low frequency dominant region in the inner SOL. In the standard divertor configuration, the broadband turbulence with a frequency range of 40–120 kHz is located near the island center along the probe path, leading to outward transport. These broadband fluctuations propagate with a velocity of 2.3–4.4 km s−1 poloidally along the ion diamagnetic drift direction in the plasma frame, with close to 0.1. The large radial transport induced by the broadband turbulence is accompanied by a steep electron density gradient. The low frequency (5–30 kHz) dominant transport exhibits obvious intermittent structure. Some statistical techniques are applied to the characterization of the intermittent transport.

Heavy ion beam probe design and operation on the T-10 tokamak

Advanced heavy ion beam probe (HIBP) operates on the T-10 tokamak with 20–130 μA Tl+ beam accelerated up to 330 keV. The HIBP has a unique capability to measure the mean value of the core plasma potential, and the oscillations in potential φ, density ne and poloidal magnetic field simultaneously in 5 spatially separated sample volumes for OH and ECRH plasmas with n¯e=(0.3−5)×1019 m−3, 100<Ipl<330 kA. Time evolution of local plasma parameters and/or radial profiles can be measured in a single shot. The profile in the range 0.25<ρ<1 is available shot by shot for B0<2.2 T. The paper describes main elements of hardware: injector, beamlines, control systems, analyzer, power supplies, and software for HIBP. Physical examples show that HIBP can measure the cross-phase of density oscillations, the poloidal phase velocity of turbulence rotation, the poloidal electric field and the radial turbulent particle flux. Spectral analysis allows us to distinguish various types of turbulence, such as broadband (<500 kHz), quasicoherent, tearing and geodesic acoustic modes.

Neoclassical and turbulent E × B flows in flux-driven gyrokinetic simulations of Ohmic tokamak plasmas

The interplay of flows and turbulence in Ohmic FT-2 tokamak plasmas is analysed via gyrokinetic simulations with the flux-driven ELMFIRE code. The simulation predictions agree qualitatively with analytical estimates for the scaling of the neoclassical radial electric field as a function of collisionality for ad hoc parameters. For the experimental parameters, the global full-f modeling agrees well with the analytical estimates in a neoclassical setting, while including kinetic electrons and impurities has a small impact. Allowing turbulence to develop modifies the flow profile through relaxation of profiles caused by turbulent transport, non-adiabatic response of passing electrons around rational surfaces, and turbulent flow drive. Geodesic acoustic mode (GAM) is the main zonal flow component in the simulations, and its frequency and amplitude agree with theoretical predictions and experimental measurements. In the simulations, the non-linear energy transfer from the turbulence to the flows through the Reynolds force is balanced by the collisional flow dissipation. Temporal relationship between the oscillating flow, Reynolds force, and turbulent particle flux is consistent with the fundamental physics picture of GAM modulating turbulent transport on the time scale of the mode. Experimental evidence also suggests anti-correlation of GAM amplitude and turbulent fluctuations.

Evaluation of Turbulent Particle Flux by Heavy Ion Beam Probe in the T-10 Tokamak

Evaluation of Turbulent Particle Flux by Heavy Ion Beam Probe in the T-10 Tokamak

Simultaneous measurements of turbulent Reynolds stresses and particle flux in both parallel and perpendicular directions in a linear magnetized plasma device.

We report temporally resolved simultaneous measurements of the turbulent Reynolds stresses in both the parallel and perpendicular directions and the corresponding particle fluxes in the fusion relevant cylindrical magnetized plasma device Controlled Shear Decorrelation eXperiment (CSDX). CSDX simulates the plasma conditions of multiple plasma instabilities that can arise in the scrape-off layer of fusion devices. In this study, we designed and used a 6-tip Langmuir probe in a novel yet simple design to simultaneously measure all the three dimensional components (radial, azimuthal, and axial) of fluctuations in velocity from the floating potentials and plasma densities with high temporal resolution. From these, we calculated the parallel and perpendicular Reynolds stress and the particle fluxes in addition to the density and potential spectra and the cross phase between different quantities. We can obtain radial profiles of all the aforementioned plasma quantities, which are extremely useful for studying plasma turbulence due to multiple instabilities. We have also cross-checked the time averaged velocity profiles from the probe with laser induced fluorescence measurements of the mean plasma velocity for some common plasma source parameters.

Dependence of the turbulent particle flux on hydrogen isotopes induced by collisionality

The impact of the change of the mass of hydrogen isotopes on the turbulent particle flux is studied. The trapped electron component of the turbulent particle convection induced by collisionality, which is outward in ion temperature gradient turbulence, increases with decreasing thermal velocity of the isotope. Thereby, the lighter is the isotope, the stronger is the turbulent pinch, and the larger is the predicted density gradient at the null of the particle flux. The passing particle component of the flux increases with decreasing mass of the isotope and can also affect the predicted density gradient. This effect is however subdominant for usual core plasma parameters. The analytical results are confirmed by means of both quasi-linear and nonlinear gyrokinetic simulations, and an estimate of the difference in local density gradient produced by this effect as a function of collisionality has been obtained for typical plasma parameters at mid-radius. Analysis of currently available experimental data from the JET and the ASDEX Upgrade tokamaks does not show any clear and general evidence of inconsistency with this theoretically predicted effect outside the errorbars and also allows the identification of cases providing weak evidence of qualitative consistency.

Intermittent strong transport of the quasi-adiabatic plasma state

The dynamics of the fluctuating electrostatic potential and the plasma density couched in the resistive-drift model at nearly adiabatic state are simulated. The linear modes are unstable if the phase difference between the potential and the density are positive. Exponential growth of the random small perturbations slows down due to the nonlinear E × B flows that work in two ways. They regulate the strength of the fluctuations by transferring the energy from the energy-producing scale to neighboring scales and reduce the cross phase at the same time. During quasi-steady relaxation sporadic appearance of very strong turbulent particle flux is observed that is characterized by the flat energy spectrum and the broad secondary peak in the mesoscale of the order of the gyro-radius. Such boost of the transport is found to be caused by presence of relatively large cross phase as the E × B flows are not effective in cancelling out the cross phase.

Gyrokinetic modelling of the quasilinear particle flux for plasmas with neutral-beam fuelling

A quasilinear particle flux is modelled based on gyrokinetic calculations. The particle flux is estimated by determining factors, namely, coefficients of off-diagonal terms and a particle diffusivity. In this paper, the methodology to estimate the factors is presented using a subset of JT-60U plasmas. First, the coefficients of off-diagonal terms are estimated by linear gyrokinetic calculations. Next, to obtain the particle diffusivity, a semi-empirical approach is taken. Most experimental analyses for particle transport have assumed that turbulent particle fluxes are zero in the core region. On the other hand, even in the stationary state, the plasmas in question have a finite turbulent particle flux due to neutral-beam fuelling. By combining estimates of the experimental turbulent particle flux and the coefficients of off-diagonal terms calculated earlier, the particle diffusivity is obtained. The particle diffusivity should reflect a saturation amplitude of instabilities. The particle diffusivity is investigated in terms of the effects of the linear instability and linear zonal flow response, and it is found that a formula including these effects roughly reproduces the particle diffusivity. The developed framework for prediction of the particle flux is flexible to add terms neglected in the current model. The methodology to estimate the quasilinear particle flux requires so low computational cost that a database consisting of the resultant coefficients of off-diagonal terms and particle diffusivity can be constructed to train a neural network. The development of the methodology is the first step towards a neural-network-based particle transport model for fast prediction of the particle flux.

Edge shear flows and particle transport near the density limit of the HL-2A tokamak

Edge shear flow and its effect on regulating turbulent transport have long been suspected to play an important role in plasmas operating near the Greenwald density limit nG. In this study, equilibrium profiles as well as the turbulent particle flux and Reynolds stress across the separatrix in the HL-2A tokamak are examined as is approached in ohmic L-mode discharges. As the normalized line-averaged density is raised, the shearing rate of the mean poloidal flow drops, and the turbulent drive for the low-frequency zonal flow (the Reynolds power ) collapses. Correspondingly, the turbulent particle transport increases drastically with increasing collision rates. The geodesic acoustic modes (GAMs) gain more energy from the ambient turbulence at higher densities, but have smaller shearing rate than low-frequency zonal flows. The increased density also introduces decreased adiabaticity which not only enhances the particle transport but is also related to reduction in the eddy-tilting and the Reynolds power. Both effects may lead to cooling of edge plasmas and therefore the onset of MHD instabilities that limit the plasma density.

Turbulent transport reduction induced by transition on radial electric field shear and curvature through amplitude and cross-phase in torus plasma

Spatiotemporal evolutions of radial electric field and turbulence are measured simultaneously in the H-mode transition, which is a prototypical example of turbulence structure formation in high-temperature plasmas. In the dynamical phase where transport barrier is established abruptly, the time-space-frequency-resolved turbulent particle flux is obtained. Here we report the validation of the mechanism of transport barrier formation quantitatively. It is found that the particle flux is suppressed predominantly by reducing density fluctuation amplitude and cross phase between density fluctuation and potential fluctuation. Both radial electric field shear and curvature are responsible for the amplitude suppression as was predicted by theory. Turbulence amplitude reduction immediately responds to the growth of the radial electric field non-uniformity and saturates, while cross phase continuously approaches zero.

Observation of radially inward turbulent particle flux in ETG dominated plasma of LVPD

Radially inward turbulent particle flux is observed in the core region of target plasma of Large Volume Plasma Device where electron temperature gradient (ETG) driven turbulence conditions are satisfied with threshold, ηETG=Ln/LT&amp;gt;2/3 [Mattoo et al., Phys. Rev. Lett. 108, 255007 (2012)]. The observed mode satisfies the scale length and frequency ordering of ETG (k⊥ρe≤1≪k⊥ρi,Ωi&amp;lt;ω≪Ωe), where k⊥ is the perpendicular wave vector, ρe ,ρi are Larmor radii of electron and ion, respectively, and Ωi,Ωe, and ω are the ion, electron gyro frequencies, and the mode frequency, respectively. The measured flux is dominantly electrostatic (Γes≈105Γem), although the nature of the turbulence is electromagnetic (β∼0.1−0.6). Experimental observations of the phase angle between density and potential fluctuations, θñ,ϕ̃, and turbulent particle flux, Γes, shows good agreement with the theoretical estimations derived for ETG turbulence.

Measurement of geodesic acoustic modes and the turbulent particle flux in the T-10 tokamak plasmas

Geodesic acoustic modes (GAMs) and the turbulent particle flux were studied in the T-10 tokamak in discharges with Ohmic (OH) and electron cyclotron heating (ECRH). The broadband oscillations of electric potential and density with frequencies up to 250 kHz were measured using a heavy ion beam probe (HIBP) in the plasma core. At the plasma edge, at a relative radius ρ > 0.8, the dominant GAM peak with a frequency of approximately 20 kHz and the noticeable peak of quasicoherent oscillations in the 40–100 kHz range were observed. Using a multislit energy analyzer, we estimate the poloidal electric field Epol and the radial electrostatic turbulent particle flux, which is driven by drift in crossed E × B fields. The GAM peak was observed in the spectrum of potential oscillations, but it was practically absent in the spectrum of Epol oscillations and in the frequency-resolved particle flux. However, the flux was observed in the broadband range. These results agree with the theoretical concept of GAM and our earlier measurements of symmetric poloidal structure of GAM potential perturbations.

Impact of a hollow density profile on turbulent particle fluxes: Gyrokinetic and fluid simulations

Hollow density profiles may occur in connection with pellet fuelling and L to H transitions. A positive density gradient could potentially stabilize the turbulence or change the relation between convective and diffusive fluxes, thereby reducing the turbulent transport of particles towards the center, making the pellet fuelling scheme inefficient. In the present work, the particle transport driven by Ion Temperature Gradient/Trapped Electron (ITG/TE) mode turbulence in hollow density profiles is studied by fluid as well as gyrokinetic simulations. The fluid model used, an extended version of the Weiland transport model, Extended Drift Wave Model (EDWM), incorporates an arbitrary number of ion species in a multi-fluid description and an extended wavelength spectrum. The fluid model, which is fast and hence suitable for use in predictive simulations, is compared to gyrokinetic simulations using the code GENE. Typical tokamak parameters are used based on the Cyclone Base Case. Parameter scans in key plasma parameters like plasma β, R/LT, and magnetic shear are investigated. In addition, the effects of a fast species are studied and global ITG simulations in a simplified physics description are performed in order to investigate nonlocal effects. It is found that β in particular, has a stabilizing effect in the negative R/Ln region. Both nonlinear GENE and EDWM simulations show a decrease in inward flux for negative R/Ln and a change in the direction from inward to outward for positive R/Ln. Moreover, the addition of fast particles was shown to decrease the inward main ion particle flux in the positive gradient region further. This might have serious consequences for pellet fuelling of high β plasmas. Additionally, the heat flux in global ITG turbulence simulations indicates that nonlocal effects can play a different role from usual in connection with pellet fuelling.

Turbulent thermal diffusion in strongly stratified turbulence: Theory and experiments

Turbulent thermal diffusion is a combined effect of the temperature stratified turbulence and inertia of small particles. It causes the appearance of a non-diffusive turbulent flux of particles in the direction of the turbulent heat flux. This non-diffusive turbulent flux of particles is proportional to the product of the mean particle number density and the effective velocity of inertial particles. The theory of this effect has been previously developed only for small temperature gradients and small Stokes numbers (Phys. Rev. Lett. {\bf 76}, 224, 1996). In this study a generalized theory of turbulent thermal diffusion for arbitrary temperature gradients and Stokes numbers has been developed. The laboratory experiments in the oscillating grid turbulence and in the multi-fan produced turbulence have been performed to validate the theory of turbulent thermal diffusion in strongly stratified turbulent flows. It has been shown that the ratio of the effective velocity of inertial particles to the characteristic vertical turbulent velocity for large Reynolds numbers is less than 1. The effective velocity of inertial particles as well as the effective coefficient of turbulent thermal diffusion increase with Stokes numbers reaching the maximum at small Stokes numbers and decreases for larger Stokes numbers. The effective coefficient of turbulent thermal diffusion also decreases with the mean temperature gradient. It has been demonstrated that the developed theory is in a good agreement with the results of the laboratory experiments.